In §, we give the main result of the paper. Let
\(K=\mathbb {Q}(\sqrt{-3})\) . In 2011, G. Han and K. Ono connect 3-core partitions
and ideals of the ring of Eisenstein integers [1]}
by proving an identity between modular forms. Ono has asked for a direct
explanation for this phenomenon. We will see that our construction allows
to describe \(\mathcal {E}_n\)  using this ring. In particular, we obtain in
Theorem REF  an explicit bijection between the set of
3-core partitions and the ideals of the ring of Eisenstein integers of
norm \(3n+1\) . This explains the result of Han and Ono.
